You will have to tap Cortana or the search button since your phone does not have 'hey Cortana
'Mpow Cheetah. You will like the way they fit on or hate it. I like.
works good, announces when you turn it on and off

There are a lot of wireless Bluetooth headsets that will allow you to activate Cortana by pressing a button. Sorry, not exclusive to wired headsets, and you're more likely to find it easier on Bluetooth.

I've got the Mpow Freego headset, and by long-pressing the multi-function button, it activates Cortana's voice mode. Most bluetooth headsets with a multi-function button will do this.

Take a look for ones with a multi-function button, pull up a PDF manual for it, and see if it supports it.

Currently i am using the LG tone+ [hbs 730] and it has been working fine. If you long press the call button it can activate Cortana. However if you pair 2 devices to the headset it will not. Thanks and hope this helps!

On a side note battery life is well over 12 hours with playing music over BT throughout the whole day and paired to an iPhone 5s for work.

Currently i am using the LG tone+ [hbs 730] and it has been working fine. If you long press the call button it can activate Cortana. However if you pair 2 devices to the headset it will not. Thanks and hope this helps!

On a side note battery life is well over 12 hours with playing music over BT throughout the whole day and paired to an iPhone 5s for work.

hey thanks a lot. Im from Sri Lanka n I visited a few shops here and found the same headset, but my gut feeling told me they are all fake. cheap plastic finish etc made me curious! can you kindly post a few pics of the packaging and the headset itself.

I also ordered a "Xiaomi Piston III Youth Edition" wired headset for current use since I wasn't satisfied with the genuinity of the bluetooth stuff here

I see you ended up wired, but I thought I'd post to show you an excellent option if you change your mind and want to go Bluetooth.

I have the LG Tones Infinim, Harman Kardon edition. The battery will go 10+ hours, they have been excellent from day one. I have had them for almost a year and a half and use them at least 5 days a week at work. The left button press is like pressing the microphone key, as if Cortana is always open. You just need to learn voice commands, or how to get her to reply without displaying a web page answer.
I think they go for close to $200 US, but mine have been worth it for sure.